In the past half-century, computers and network technology have become prevalent in all aspects of our daily lives. Electronic mail (email), remote video conference, online music, online movies, and other applications are now commonplace in this digital age. Online personal albums and data storage are widely used and are easily accessed and shared across the internet. To improve the quality of service and reduce record storage costs, many medical institutions and hospitals digitize and store diagnostic images and/or the medical records of their patients. This information can be shared and transmitted over networks from the laboratories to medical centers or to a doctor's office. However, the privacy of these images and data is susceptible to unauthorized used and might be disclosed to some unauthorized individuals. While the degree of security required may vary for various applications, it is generally important for all of these examples that the substance of particular communications passes from a sender to an intended receiver without other parties being able to interpret the transferred message. In addition, there are further instances where information must be protected from snoopers who have access to the information through data processing networks. Therefore, digital images should be encrypted, e.g., for storage or for transmittal over network.
Many image scrambling and image encryption algorithms have been developed based on different principles. Generally these algorithms can be divided into two categories based on the type of encryption domain implemented in the algorithm, namely the transform domain and the spatial domain. In transform domain encryption, the image first is transformed to some frequency domain and then encryption is applied and the image is transformed back to a spatial domain image. Dang et al. proposed his approach based on the Discrete Wavelet Transform (“Image encryption for secure Internet multimedia applications,” 2000, Consumer Electronics, IEEE Transactions on, 46(3), 395-403). Hui et al. gave an encryption algorithm with fractional discrete cosine and sine transform (“Methods for encrypting and decrypting MPEG video data efficiently”, ACM (Boston, Mass., 1996)). In contrast, in spatial domain encryption, the algorithm directly modifies image pixels. Fridrich et al. employed a 2D chaotic baker map (“Image Encryption Based on Chaotic maps”, 1997, IEEE International Conference on Systems, Man, and Cybernetics, 1105-1110). Zou et al. applied a classical Fibonacci number to scramble images in the spatial domain (“A new digital image scrambling method based on Fibonacci numbers”, 2004, Circuit and Systems 3: 965-968). Zhang et al. used discrete Chebyshev chaotic sequences (“Discrete Chaotic Encryption and Decryption of Digital Images”, 2008, Computer Science and Software Engineering, International Conference on, 849-852).